In this state, every vote counts, which is why President Obama is contesting even the areas he has no chance of winning. A case in point: Colorado Springs, in El Paso County, a place with five military installations and deep evangelical roots. Both Democrats and Republicans say the community will hand the president a major defeat on Nov. 6.

Undaunted, Obama’s campaign continues to pour money and resources into this beautiful and deeply conservative area at the base of Pike’s Peak.

Obama won Colorado by nine points in 2008, but Romney now leads by a fraction of a percentage point, 47.8 to 47.6, according to an average of recent Colorado polls. If the president can shrink the margin here in El Paso County by even a little — he lost by 19 points in 2008 — he might be able to keep Colorado blue, his supporters argue.

“It makes me work harder and makes me a bit more dedicated than if it were incredibly easy,” said Rozanne David, 69, an Obama team leader in the suburb of Black Forest.

That means tens of thousands of door knocks and phone calls to registered Democrats and unaffiliated voters. It also means following up on the deluge of advertising that has vaulted Colorado Springs, a city of 426,000 people, into the 10 top media markets for political ads in the country.

In one week here in mid-September, for example, the number of television ads about the presidential race had nearly tripled, to 1,445, from the same period in 2008, according to data provided to National Public Radio from Kantar Media. During that week, Democratic ads outnumbered Republican ones, 757 to 688.

For a second-tier market, the effect can be numbing.

“I’m getting a bit irritated,” said Robin Curry, 55, a bartender at the American Legion post and a Vietnam-era veteran.

Bill Houghton, 68, who sits on the board of the Colorado Mountain Club, used pantomime to show his annoyance. Extending his arm, he pressed the mute button on an imaginary remote control.

Both men plan to vote for Obama, but they recognize they are in the minority in El Paso County. “I’m not the shining star around here,” Curry said, looking around an empty Legion hall on a cold afternoon.

“I don’t think Romney’s got a clue,” Curry said. “I know for a fact that corporate America is no way to run this country.”

But many Colorado voters believe that mind-set is exactly what the country needs, said Chris Walker, a Romney campaign spokesman.

“When you talk to people on the ground, there’s a level of disappointment in the last four years,” Walker said. “People are looking for a change in leadership.”

To solidify that support, Romney and his running mate, Representative Paul Ryan, appeared in the Denver area on Tuesday. Ryan has spoken in Colorado Springs several times, Walker said.

The Republican ticket is attracting support from the military community here because of concerns about large, automatic cuts in defense spending, scheduled to take effect in January, that Congress approved to resolve the debt-ceiling crisis.

Although Republicans agreed to the cuts, as well as an equal cut in domestic spending, Romney has repeatedly assailed the president on the plan during rallies in states with a large military presence, such as Colorado and Virginia.

“People are thinking that’s just the wrong priority,” Walker said.

That sentiment was echoed by Jerry Rutledge, who owns a downtown clothing business that features a large Romney/Ryan sign on its outdoor facade.

“I like his energy policy. I like his tax policy,” Rutledge said of Romney. “To me, it’s all about the economy and jobs. We need to get this economy squared away.”

Questions about Romney’s shifting stance on issues such as abortion and gun control do not concern him. “It’s not on my radar,” Rutledge said.

Instead, the overriding issue is Obama, whose negatives appear to be more of a factor for Rutledge than Romney’s positives.

“I think it’s easier to talk about Obama. By and large, the country really doesn’t want his brand of socialism,” Rutledge said. “Obamacare was passed in the most disgusting manner. There certainly was no bipartisanship. He’s a very divisive man, maybe the most divisive president ever.”